Electric displacement

The electric displacement is an auxiliary field defined as

⃗ 𝐃 = 𝜖 0 ⃗ 𝐄 + ⃗ 𝐏

where $⃗ 𝐄$ is the electric field and $⃗ 𝐏$ is the electric polarization density. $⃗ 𝐃$ satisfies Gauß's law for diëlectrics which is analogous to Gauß's law satisfied by $⃗ 𝐄$ , however unlike $⃗ 𝐄$ its curl does not in general vanish ( $⃗ \nabla \times ⃗ 𝐃 = ⃗ \nabla \times ⃗ 𝐏$ ).

Linear media

In the special case of a Linear diëlectric

⃗ 𝐃 = 𝜖 ⃗ 𝐄

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